Humidity Ratio Calculator

The humidity ratio w, also called the mixing ratio, is the mass of water vapor carried by each unit mass of dry air, and it follows from Dalton's law of partial pressures. Moist air is treated as a mixture of dry air at partial pressure P minus e and water vapor at partial pressure e, so the mass ratio becomes a pressure ratio scaled by the ratio of molar masses, 18.015 divided by 28.965, which equals 0.622. That single constant is why w = 0.622 e / (P - e) rather than a simple ratio of pressures. The actual vapor pressure e comes from relative humidity times the saturation vapor pressure es, evaluated here with the Magnus form es = 6.112 exp(17.67 T / (T + 243.5)) in hPa. Typical values give useful anchors: indoor comfort conditions near 22 degrees C and 50 percent RH give roughly 8 g/kg, humid Gulf Coast air in July often exceeds 20 g/kg, and cold polar air falls below 1 g/kg. ASHRAE comfort envelopes are commonly bounded near 12 g/kg on the humid side. Because w is referenced to dry air mass rather than total mass, it is conserved during dry adiabatic ascent and during sensible heating, which is exactly why psychrometric charts use it as the vertical axis. The main caveats are that the Magnus fit degrades below about -30 degrees C, that saturation over ice differs from saturation over supercooled water below freezing, and that the denominator P - e makes w sensitive to the pressure entered: using sea level pressure at a mountain site can bias the result by several percent.

Quantitative psychrometry grew out of nineteenth century laboratory work on vapor pressure. Heinrich Gustav Magnus published an empirical exponential fit to measured saturation vapor pressure in 1844, and Henri Victor Regnault carried out the precise vapor pressure and hygrometric measurements against which later formulas were calibrated. The thermodynamic basis had already been laid by the Clausius-Clapeyron relation, developed by Benoit Paul Emile Clapeyron in 1834 and placed on firm footing by Rudolf Clausius in the 1850s, which explains the near exponential rise of saturation vapor pressure with temperature. The humidity ratio became an engineering variable through Willis Carrier, whose 1911 paper Rational Psychrometric Formulae, presented to the American Society of Mechanical Engineers, tied dew point, wet bulb temperature and moisture content together and introduced the psychrometric chart still used in air conditioning design. Richard Mollier developed a related enthalpy-moisture diagram in Germany in the 1920s, and both chart traditions persist today in different regions. ASHRAE has published and periodically revised psychrometric tables and equations in its Handbook of Fundamentals since the mid twentieth century, while the World Meteorological Organization standardized humidity reporting for weather stations. Sling psychrometers have since given way to capacitive polymer sensors and chilled mirror hygrometers, but the defining equation for w is unchanged.